46 research outputs found
Almost Optimal Stochastic Weighted Matching With Few Queries
We consider the {\em stochastic matching} problem. An edge-weighted general
(i.e., not necessarily bipartite) graph is given in the input, where
each edge in is {\em realized} independently with probability ; the
realization is initially unknown, however, we are able to {\em query} the edges
to determine whether they are realized. The goal is to query only a small
number of edges to find a {\em realized matching} that is sufficiently close to
the maximum matching among all realized edges. This problem has received a
considerable attention during the past decade due to its numerous real-world
applications in kidney-exchange, matchmaking services, online labor markets,
and advertisements.
Our main result is an {\em adaptive} algorithm that for any arbitrarily small
, finds a -approximation in expectation, by
querying only edges per vertex. We further show that our approach leads
to a -approximate {\em non-adaptive} algorithm that also
queries only edges per vertex. Prior to our work, no nontrivial
approximation was known for weighted graphs using a constant per-vertex budget.
The state-of-the-art adaptive (resp. non-adaptive) algorithm of Maehara and
Yamaguchi [SODA 2018] achieves a -approximation (resp.
-approximation) by querying up to edges per
vertex where denotes the maximum integer edge-weight. Our result is a
substantial improvement over this bound and has an appealing message: No matter
what the structure of the input graph is, one can get arbitrarily close to the
optimum solution by querying only a constant number of edges per vertex.
To obtain our results, we introduce novel properties of a generalization of
{\em augmenting paths} to weighted matchings that may be of independent
interest
Third-Party Data Providers Ruin Simple Mechanisms
Motivated by the growing prominence of third-party data providers in online
marketplaces, this paper studies the impact of the presence of third-party data
providers on mechanism design. When no data provider is present, it has been
shown that simple mechanisms are "good enough" -- they can achieve a constant
fraction of the revenue of optimal mechanisms. The results in this paper
demonstrate that this is no longer true in the presence of a third-party data
provider who can provide the bidder with a signal that is correlated with the
item type. Specifically, even with a single seller, a single bidder, and a
single item of uncertain type for sale, the strategies of pricing each
item-type separately (the analog of item pricing for multi-item auctions) and
bundling all item-types under a single price (the analog of grand bundling) can
both simultaneously be a logarithmic factor worse than the optimal revenue.
Further, in the presence of a data provider, item-type partitioning
mechanisms---a more general class of mechanisms which divide item-types into
disjoint groups and offer prices for each group---still cannot achieve within a
factor of the optimal revenue. Thus, our results highlight that the
presence of a data-provider forces the use of more complicated mechanisms in
order to achieve a constant fraction of the optimal revenue
A Permutation-Equivariant Neural Network Architecture For Auction Design
Designing an incentive compatible auction that maximizes expected revenue is
a central problem in Auction Design. Theoretical approaches to the problem have
hit some limits in the past decades and analytical solutions are known for only
a few simple settings. Computational approaches to the problem through the use
of LPs have their own set of limitations. Building on the success of deep
learning, a new approach was recently proposed by Duetting et al. (2019) in
which the auction is modeled by a feed-forward neural network and the design
problem is framed as a learning problem. The neural architectures used in that
work are general purpose and do not take advantage of any of the symmetries the
problem could present, such as permutation equivariance. In this work, we
consider auction design problems that have permutation-equivariant symmetry and
construct a neural architecture that is capable of perfectly recovering the
permutation-equivariant optimal mechanism, which we show is not possible with
the previous architecture. We demonstrate that permutation-equivariant
architectures are not only capable of recovering previous results, they also
have better generalization properties